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arXiv:1507.00381 · Physical Review A

Modulating carrier and sideband coupling strengths in a standing-wave gate beam

Thomas E. deLaubenfels, Jan‐Karl Burkhardt, Grahame Vittorini, J. True Merrill, Kenneth R. Brown, Jason Amini

Published Dec 10, 2015• 12 citations
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Abstract

We control the relative coupling strength of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions with the cycles for the two cases ${180}^{\ensuremath{\circ}}$ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum simulation and quantum control. Using the standing-wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.

DOI
10.1103/physreva.92.061402

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We control the relative coupling strength of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions with the cycles for the two cases 180\ensuremath∘{180}^{\ensuremath{\circ}}180\ensuremath∘ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum simulation and quantum control. Using the standing-wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.
The purpose of this work is to investigate methods by which the quantum states of trapped ions may be better controlled and measured for the applications of quantum computing, quantum simulation, and the generation of atomic frequency standards. We report on two primary projects: first, we control the relative coupling strengths of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding the technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions, with the cycles for the two cases 180◦ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum computation and quantum simulation. Second, we investigate methods proposed in Ref. [36] which may improve the performance of trapped ion (or atom) frequency standards when the interrogating local oscillator is of limited quality. These methods could be applied to future generations of small-scale frequency standards, which are in demand for applications such as local GPS networks and distributed sensors. We propose a scheme for implementing these methods in a 40Ca+ based frequency standard, and outline the technical requirements for doing so. Finally, we present preliminary results characterizing single-ion coherence times and ion “state destruction” events in our system, and discuss how they will affect the realization of the proposed scheme.
Using a single calcium ion confined in a surface-electrode trap, we study the interaction of electric quadrupole transitions with a passively phase-stable optical standing wave field sourced by photonics integrated within the trap. We characterize the optical fields through spatial mapping of the Rabi frequencies of both carrier and motional sideband transitions as well as ac Stark shifts. Our measurements demonstrate the ability to engineer favorable combinations of sideband and carrier Rabi frequency as well as ac Stark shifts for specific tasks in quantum state control and metrology.
With the recent surge for an experimentally viable quantum computer, trapped ions have come to the forefront as one of the most practical systems from which to construct a quantum computing architecture. This work has continued to explore the feasibility of using trapped ions as quantum bits, addressing the issue of quantum decoherence due to non-resonant excitation by studying the spectroscopy of a trapped ion through a standing wave. \n \nThe standing wave studied in this thesis was formed on the face of a surface-electrode ion trap held at cryogenic temperatures. Although the trap was not built with a reflective surface in mind, a lower bound on the fringe visibility was measured to be 0.717. By moving the ion through the nodes and anti-nodes of the wave, the carrier and sidebands of the S_1/2 to D_5/2 transition, commonly used for information storage, were selectively stimulated and suppressed.
All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing 88Sr+^{88}{\mathrm{Sr}}^{+}88Sr+ ions in a $\ensuremath{\lambda}=674\text{ }\text{ }\mathrm{nm}$ standing wave, whose relative position is controlled to $\ensuremath{\approx}\ensuremath{\lambda}/100$, we suppress the carrier coupling by a factor of 18, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave M\o{}lmer-S\o{}rensen gates; we use the standing wave to surpass this limit and achieve a gate duration of $15\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{s}$, restricted by the available laser power.
We present a surface-electrode Paul trap featuring integrated photonics elements, where ions are illuminated with two interfering beams at 729 nm forming a standing wave along the trap axis. In this field configuration, it is possible to excite the motional sidebands of a trapped ion while suppressing the off- resonant coupling to the corresponding carrier transition. This is of particular interest for quantum information processing, as it would allow implementing faster and lower error Mølmer-Sørensen entangling gates.We characterize the optical properties of the chip by scanning with sub-wavelength resolution the position of a single ion through the standing wave and observing Rabi oscillations for carrier and first motional sideband of different quadrupole transitions. We characterize both the strength of resonant couplings and the AC Stark shift induced by off-resonant couplings. We measure noise and drifts in the ion position and observe high stability in the standing wave profile without the need for active phase stabilization.Integrated optics allow to reliably reproduce the same field configuration in different regions of the chip, opening the way for implementing distributed, parallel quantum operations. We show the ability to control ions in different regions of the trap at the same time. We implemented real-time control of the DC voltages controlling the axial configuration of the trapping potential which enables us to load multiple ion crystals, merge, split, and shuttle them across the device.
We demonstrate minimization of ion micromotion in a linear Paul trap with the use of a high finesse cavity. The excess ion micromotion projected along the optical cavity axis or along the laser propagation direction manifests itself as sideband peaks around the carrier in the ion-cavity emission spectrum. By minimizing the sideband height in the emission spectrum, we are able to reduce the micromotion amplitude along two directions to approximately the spread of the ground state wave function. This method is useful for cavity QED experiments as it describes the possibility of efficient 3-D micromotion compensation despite optical access limitations imposed by the cavity mirrors. We also show that, in principle, sub-nanometer micromotion compensation is achievable with our current system.